Signed Roman Edgek-Domination in Graphs

• Autorzy: Leila Asgharsharghi , Seyed Mahmoud Sheikholeslami , Lutz Volkmann
• Języki publikacji: EN

Abstrakty

EN

Let k ≥ 1 be an integer, and G = (V, E) be a finite and simple graph. The closed neighborhood NG[e] of an edge e in a graph G is the set consisting of e and all edges having a common end-vertex with e. A signed Roman edge k-dominating function (SREkDF) on a graph G is a function f : E → {−1, 1, 2} satisfying the conditions that (i) for every edge e of G, ∑x∈NG[e] f(x) ≥ k and (ii) every edge e for which f(e) = −1 is adjacent to at least one edge e′ for which f(e′) = 2. The minimum of the values ∑e∈E f(e), taken over all signed Roman edge k-dominating functions f of G is called the signed Roman edge k-domination number of G, and is denoted by γ′sRk(G). In this paper we initiate the study of the signed Roman edge k-domination in graphs and present some (sharp) bounds for this parameter.

Słowa kluczowe

EN

signed Roman edge k-dominating function; signed Roman edge k-domination number

Kategorie tematyczne

• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2017
• Tom: 37
• Numer: 1
• Strony: 39-53

Daty

wydano

2017-02-01

otrzymano

2015-06-15

poprawiono

2016-02-08

zaakceptowano

2016-02-08

online

2017-01-13

Twórcy

autor

Leila Asgharsharghi

• Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R.

autor

Seyed Mahmoud Sheikholeslami

• Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R.

autor

Lutz Volkmann

• Lehrstuhl II für Mathematik, RWTH Aachen University, 52056 Aachen,

Identyfikatory

DOI

10.7151/dmgt.1912